A=(3x+4)(5x+6)

Solution for A=(3x+4)(5x+6) equation:

=(3A+4)(5A+6)

We move all terms to the left:

-((3A+4)(5A+6))=0

We multiply parentheses ..

-((+15A^2+18A+20A+24))=0


We calculate terms in parentheses: -((+15A^2+18A+20A+24)), so:

(+15A^2+18A+20A+24)

We get rid of parentheses

15A^2+18A+20A+24

We add all the numbers together, and all the variables

15A^2+38A+24

Back to the equation:

-(15A^2+38A+24)


We get rid of parentheses

-15A^2-38A-24=0

a = -15; b = -38; c = -24;
Δ = b2-4ac
Δ = -382-4·(-15)·(-24)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2}{2*-15}=\frac{36}{-30}
=-1+1/5
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2}{2*-15}=\frac{40}{-30}
=-1+1/3
$